Hello,
This kitty is very lucky to have you!! You have several options open to you at this point. First, you can call around to vets in your area and see if they would be open to treating a potentially feral kitty with a possible broken leg....you will need to decide how far you want to go, because once trapped kitty will likely need to be completely sedated before he or she can be safely examined. If a fracture is found, are you willing to treat it surgically (if necessary)? Do you want to test this kitty for leukemia and aids, and euthanize if the tests come up positive? If you are willing to take some responsibility for this kitty and can find a vet that will help, you can try to humanely trap he or she in a have a heart trap, which is available at your local pet co or pet smart, or your local humane society may have the traps for rent. Don't feel that you need to put this kitty through surgery for a badly broken leg if it is beyond your financial means, and don't feel that you need to keep this kitty alive with a serious viral infection (like leukemia or aids) no matter what. Sometimes humane euthanasia is the lesser of all evils, and sometimes it can be avoided.
While you are probably correct in assuming that animal control will euthanize this kitty, there may be organizations in your area that can help. However, the final result might be the same if the kitty is too badly injured to be put back in the wild. You can check out the following organization, alley cat allies, and they may be able to help with this kitty.
www.alleycat.org
Please let me know if I can be of further assistance. If this has been helpful, please hit the green accept button. Best of luck with your little foundling, I hope things work out :)
Emergency Critical Care Nurse
16+ years of veterinary experience